XIV. Congress of the International Society for Photogrammetry,
Hamburg 1980
Commission VII
Working Group VII/7
Presented Paper
OBJECT- DEPENDENT SPATIAL VARIATIONS OF SPECTRAL
SIGNATURES ON INFRARED COLOUR AERIAL PHOTOGRAPHS
W . Schneider and A . Lantschner
Institut fUr Vermessungswesen und Fernerkundung
UniversiHit fUr Bodenkultur
Vienna,
Austria
Abstract
Methods for determining object -specific spatial distributions of colour
density on aerial photographs are described. The distributions are
obtained by adjustment calculation from density measurements on sample
areas imaged at least twice on neighbouring photographs.
Examples of data on space -dependent colour densities of tree species
deduced by these methods are presented . Improvements in classification
accuracy after preprocessing steps compensating these spatial variations
are demonstrated. Finally,
a
classification method making deliberate
use of the object -specific spatial distributions of colour density is
described.
8:1.9.
1 . Introduction
Infrared colour aerial photographs represent, in a qualified sense,
three -channel radiometric data that can be used for automatic object
identification and thematic mapping . A major difficulty, however,
arises from the fact that spectral signatures of objects usually depend
on the view angle (o/. 1 ~) at which the objects are sensed , and hence
on their position (x 1 ;r) on the aerial photograph .
As a consequence of this spatial variation of signatures, clusters of
object classes in the three -dimensional signature space tend to spread
out, thus affecting the selectivity of a classific ation based on these
signatures .
It is therefore highly desirable to obtain detailed information on the
space -dependence of signatures in order to be able to compensate it
in a preprocessing step .
In principle one could try to quantify the individual components contributing to this space dependence , such as
view -angle dependent object reflectivity (mainly caused by a viewangle depend ent ratio of sun-lit and shadowed areas) ?(d
1-
0)
atmospheric transmission
TA
(d.,0) [4]
atmospheric path radiance (haze)
1
[ 3],
J
EA {d. 1 ~) [~] J
off -axis illumination loss of camera lens and filte r s
J.
and non -uniform development [ G
T r acing the image formation process from the illumination conditions
of the scene to the final development of the photographic image, one
could then dete rmine the overall effect of spatial density variation on
the aerial photograph :
1
f (j)
E(jJ.
·
+
)) ·
·t
( 1)
D~j) (x ;J) =
1
[x1 1 , (
)(jr<><~~) -z:-~)(~,0) E~ (~1 fo t-~j)(oZ 1 fo)
J.
(.)
D/
In this equation, j denotes the spectral channel,
{x 1~) is the colour
density of object i in .spectral channel j measured at position (x,~)
on the photograph, f(J) (x,"J', E) represents the ~space -dependent transfer
characteristic of the photographic materi al, t:. tJ) is the i rr adiance of
the scene in channel j , and t is the exposure time .
This procedure,
practice .
however ,
wo uld be too complicated to be applied in
On the other hand, it is possible to derive the spatial variations of
signatures directly from a set of objects each of which is imaged at
least twice in the overlapping regions of neighbouring photographs. In this
communication, a new method based on this idea is described in the
820.
context of other techniques for determining spatial signature variations .
Data on space -dependent colour densities of tree species deduced by
this method are presented. Improvements in classification accuracy
after preprocessing steps compensating these spatial variations are
demonstrated . Finally, a classification method making deliberate use
of the object -specific spatial dependence of spectral signatures is
described (as proposed e . g . in [1] ).
2. Determination of the spatial variation of signatures by adjustment
calculation
In the following, it is assumed that the objects to be identified on
aerial photographs can be classified into distinct categories.
The
spatial dependence of the colour densities of all objects belonging to
a given category A may be described by functions
(')
D~J(x 1 ·J')
(')(
=
3~
(j)
D[o 1 X1'J
)
;
(2)
.Di!)
where
is the "standardized" density for colour j of object i
(colour density that would have been observed for object i located
at position (0, 0) ) . No assumptions are made on the homogeneity of
the colour densities within one category (e.g . tree species). It can
even be divided into subclasses (e.g . according to degree of stress)
of distinguishable spectral signatures, as long as the functions
describing the spatial variations of signatures are identical for all
subclasses .
The image coordinate system is assumed to have its ong1n at the
principal point of the image, with the x -axis parallel to the direction
of incident sunlight (fig. 1). In this case it can be assumed that the
spatial variations of signatures (except the contribution of nonuniform
development) is symmetrical with respect to the x-axis, i.e., the
corresponding functions are even functions of y.
X
Fig. 1: Image coordinate system
82:1..
In order to be able to determine functions 9~)
by adjustment calculation from measurements on the aerial photographs, certain assumptions concerning the type of these functions have to be made. Using
the model described by equ. (1), the following cases can be
distinguished (index j is omitted from now) :
a) Linear relationship between density D and the logarithm of exposure :
( 3)
In equ . (3), K(x,~) represents the segment of the
characteristic curve on the density axis, and '{(X 1 d)
is the gradation [ 6
J.
This assumption will be satisfied mainly for low-contrast
black -and -white films . For colour films only under certain
circumstances (low contrast objects, optimum exposure
conditions) .
aa) Uniform photographic development conditions : ;y-(J<. 1 ~) =-'fv 1 k(x,~) =- i<c.
Films processed by automatic processing machines will
more likely satisfy this condition than films processed by
rewind methods .
aaa) Negligible atmospheric path radiance : EA = 0 .
This case may apply at clear weather conditions, at low
sun angles, and for long -wavelength channels . Only
multiplicative factors are left, which modify the irradiance
(i.e . , additive terms modifying the photographic density) [ 8] :
Dl(x,",t)
= D~o
-t-
a(x 1'}).
( 4)
aaaa) Quasi -random distribution of samples of the various
subclasses of one category [ 8] : The average signal at each
position (x,'t) on the photograph (calculated by multiple
regression) then is a measure of the spatial dependence
of the signatures . If an adjustment function of second
degree of the form Q 0 +- a 1 x + a1. x1 + o.. 3 "j 2. (in agreement
with the above -mentioned symmetry with respect to the
x - axis) is determined, then the additive term of equ . (4)
is obtained as
(5)
822.
aaab) Arbitrary distribution of samples of the various subclasses
of one category: For every pair of density values D.(x,,1J~)
.D( ('i-1- 1 "j-2-)
obtained from one and the same object imaged
in the overlapping region on two adjacent photographs the
difference between the "standardized'' densities ~Di.o
calculated from both values according to equ. (4) should be
a minimum . Again substituting a second -degree polynomial
for o.(x,"t) , the unknown coefficients a,, o.~.., u 3
can
be calculated by adjustment of the "observation equations"
aab) In the presence of atmospheric path radiance it is advisable
to take the antilogarithm of equ. (3) substituted in equ. (1)
and to work with irradiances L8]:
(I)
The spatial variations of the irradiances are no '
characterized by a multiplicative and an additive term
(the latter representing the influence of atmospheric path
radiance, modified by off -axis lens losses) :
(8)
For every pair of irradiance values [t (x1 1 ~1 ), [ , ( x t 1 ·~ L)
obtained from one and the same object imaged in the overlapping region on two adjacent photographs one observation
equation of the form
[.(x ·"'/)
L
= Ei(x'l.,~,_)- Q()(~_, 1 ~~..) • m(x,'111) + u..(x 11 "-l1)
+v-
m(x:~,,~L)
'I d1
is obtained. Substituting
a
o. h~)
(9)
d
according to equ. (5) and
(1 0)
the unknown coefficients a~, aL 1 ct 1 , VVl 11 m2. 1 VY1 3
obtained b, adjustment of observation equations .
can be
7
ab) Nonuniform photographic de ·elopment conditions :
This case can be treated in analogy to aab), if the photographic nonuniformities (functions y-{x 1'J') and K(x.,'f) )
are known. This case has also been dealt with in detail by
Sievers [ 6
J.
823.
b) Nonlinear relationship between D and log (E·t) :
Inspection of typical characteristic curves of infrared
colour films (fig . 2) [ 9} reveals that the postulate of a
linear relationship bet\veen D and log (E ·t) often is not
valid in practice . As an example, on the aerial photographs used for this investigation the ave rage sun -lit
scene has densities corresponding to exposure E1·t as
shown in fig . 2, while the average shadowed scene has
densities corresponding to exposure Et·t . Taking into
account that , especially on forest aerial photographs, the
fraction of sun -lit portions of one and the same homogeneous
sample area may, depending on the view angle , vary
between almost 0 % and almost 100 o/o, it becomes clear
that a nonlinear relationship D - log (E·t) must be assumed .
D
3
2
Fig. 2
1
In this case,
log(E. t)
Characteristic curves
of infr ared colour
film [9]
a purely empirical function
(11)
with polynomials OL(x,~) and m.{x,'j) according to equs.
(5) and (1 0) may be postulated . The coefficients of these
polynomials can be obtained by adjustment of observations
in complete analogy to aab) .
3 . Examples of spatial variations of colour densities on forest aerial
photographs
The photographs used for this investigation were taken on Aerochrome
Infrared film 2443 with a Wild RC-10 camera equipped with an Aviotar
f = 30 em lens, from a height of approximately 2100 m above ground.
Approximately 200 homogeneous sample areas of beech, spruce and
pine stands were localized in the field and on the photographs . On the
average, every sample area could be identified on three neighbouring
photographs. Colour density measurements at the resulting 600
positions on the photographs were performed using a densitometer
Macbeth TD 504 with measuring apertures varying between 1 mm and
3 mm, depending on the size of the homogeneous sample areas .
B2q.
Image coordinates of the sample areas were determined and transformed
to a coordinate system oriented relative to the direction of incident
sunlight according to fig . 1 .
The spatial variations of the colour densities of the different tree
species were computed according to the methods described above . As
an example, functions m (x,~) and o..(x 1 ~) of equ. (11) are reproduced
in fig . 3 for colour channel blue and ~ree species beech and spruce.
The "standardized'' density values :Di~l of individual sample areas,
calculated with the aid of these functions from density measurements
..D,iil(x 1'a)
at different positions on the photographs, have standard
deviations as low as 0 · 02, 0 · 03 and 0 · 04, depending on colour channel
and tree species . It must be stressed that, despite of this excellent
degree of "standardization", deviations between density values of
different sample areas within one category are not reduced . The full
information content of the data with respect to further differentiation
of samples within one category therefore is maintained .
I
1 a(x,
m(x, y)
beech
~
y)
y
~y
beech
/
/
X
X
f
spruce
a(x, y)
spruce
/
/
X
X
Fig . 3: Multiplicative and additive density variation functions for
colour channel "blue"
825.
4 . Improvements in classification accuracy by compensating spatial
density variations
Compensation of spatial variations of densities is a useful preprocessing
method in order to improve the selectivity of a subsequent classification
process . Strictly speaking, the "standardization" of density values
according to the methods desc r ibed above can be performed only for
one catego r y of objects (e . g . tree species) . If, however, a standa r dization
algorithm for object category A is applied to an entire image, the
overlap between object category A and the other categories in density
space is nevertheless reduced .
In order to demonstrate this, plots of the one - <J - boundaries of
clusters of 3 tree species in "standardized" colour density spaces
are r eproduced in fig. 4 . For comparison, a plot of clusters obtained
after p r eprocessing by ratioing [ 10 is included .
J
w
1.00
w
--'
Ill
::J
>~
1.01!
::J
...J
Ill
.7<:.
l!1
:z
w
Q
.<:.0
>r-
5EE~
Ui
SPRUCE
.7S
v ~
z
w
BEECH
Q
.Ski
PINE
PINE
.2<:. ...___ _ _ _ _ _ _ _ _ _ _ _ _ __
.2S .._ _ _ _ _ _ _ _ _ _ _ _ _ _ __
lo1
r;
DENSITY RED
DENS! TY RED
a)
w
b)
1.00
w
--'
Ill
>r-
iJ1
ll
!:::
::J
0
:I;
:z
.7S
l!1
::J
SPRUCE
:z
~
v ~
w
.SJ.l
::J
...J
"'
PINE
"!
lo1
r;
lSI
~
SPRUCE
-:'ill
w
0
"!
lSI
~INE
ui
:z
.2S
lo1
BEECH
"'
w
BEECH
Q
.0,2S
lo1
':'!
lo1
lSI
'::1
'::!
DENSITY RED
..
-:7S
"',.
lrl
lSI
lrl
"!
"1
DENS. RED MINUS WHITE
d)
c)
Fig . 4: One - a- -boundaries of clusters in colour density spaces :
a) original densities, b) densities corrected according to equ . (11)
for beech, c) densities corrected according to equ . (11) for spruce,
d) differences of densities (corresponding to ratios of i r radiances) .
826.
5 . Classification based on object -specific spatial variations .of signatures
Sample areas in the o v erlapping region of neighbouring photographs can
be classified on the basis of differences in the spatial variation of densities, provided that density values from at least two different photographs are available for every sample area :
Every density value ]t(x 1'j) of a sample ar e a of unknown category is con,-erted to "standardized" density values D; 0 under the assumptions that
the sample area belongs to categories A, B, C etc. The sample area is
then assigned to the category with the minimum standard deviation of the
values of _D; 0 calculated from the various (at least two) values of D, (x, J)
This method has been tested using pairs of density measurements made
with white light on neighbouring photographs. In fig. 5, the frequency
distributions of the quantity
6
'=
In,1S- D~tsl
-
D~l-B I
t ]dB -
(12)
are shown for sample areas of beech and of spruce. In equ. (12),
.D<1 B and .D~tB ( :U, 1 s and ];,_ 5 ) are the "standardized'' density values
calculated from density values of the same sample area measured on
neighbouring photographs at positions 1 and 2, respectively, under the
assumption that the sample belongs to category beech (spruce). It can
be seen from fig. 5 that approximately 75 % of all samples could be
classified correctly.
No spectral information is used for this classification. The discrimination
between the two categories is possible because of the different form of
canopy surfaces of beech and spruce stands, which influences the viewangl e -dependent ratio of sunlit and shadowed areas.
f
spruce
I
0
C')
I
0
N
I
I
I
I
beech
I
0
......
0
0
......
0
N--- 6.
827.
Fig. 5: Classification
according to spatial
density variation
features
6 . Conclusions
Methods for determining the spatial d istributions of colour density on
aerial photographs from density measu r ements on sample areas imaged
at least twice on neighbouring photographs have been described. No
assumptions are necessary concerning the distribution of sample areas
on the photographs .
It has
been demonst r ated that information on spatial distributions of
colour densities thus obtai ned is important
a) for the compensation of disturbing density variations prior to
automatic photointerpretation .
b) for classification methods making deliberate use of objectspecific spatial variations .
Further investigations mainly on the problem of the optimum degree of
the polynomials used in the adjustment computations are necessary .
References
[1]
Hildebrandt, G .: Die spektralen Reflexionseigenschaften der Vegetation.
Remote Sensing in Forestry. Proc . of the Symp. held during the
XVI. IUFRO World Congress, Oslo, June 1976, p 9 - 22 .
Richardson, A . J . , et al .: Plant , Soil, and Shadow Reflectance Components
of Row Crops . Phot . Eng . and Rem . Sens ., 41 (1975), p 1401 -7.
Hoffer, R .M., Holmes, R . A., Shay, J . R .: Vegetative,Soil, and Photographic Factors Affecting Tone in Agricultural Remote Multi spectral Sensing . Proc . 4th Int. Symp . on Remote Sensing of
Environm., 1966, p 115-34 .
Turner, R . E ., Malila, W . A . , Nalepka, R . F .: Importance of Atmospheric
Scattering in Remote Sensing (or Everything You Always Wanted to
Know About Atmospheric Scatter ing But Were Afraid to Ask). Proc.
7th Int.Symp . on Remote Sensing of Environm . , 1971 , p 1651 - 97 .
Bahr, H . - P .: Analytische Bestimmung und digita l e Korrektur des Licht abfalls in Bildern eines Hochleistungsobjektivs . BuL 47 (19 79) p 81 -7 .
Sievers, J. : Dens ity Corrections and Directional Reflectances of Terrain
Objects from Black-and-White Aerial Photos. Photogrammetria 33
(1977) p 95 - 112 .
[7]
Steiner, D . , Haefner, H .: Tone Distortions for Automated Interpretation .
Phot . Eng . 31 (1965) p 269 - 8 .
[8]
Nalepka, R . F., Morgenstern, J.P .: Signature Extension Techniques
Applied to Multispectral Scanner Data . Proc . 3th Int. Symp . on
Remote Sensi ng of Environm . , 1972, p 881 - 93 .
Kodak Data for Aerial Photography . Kodak Publication No . M -29 .
Quie1, F .: Zur Vorverarbeitung multispektraler Daten . BuL 44 (1976)
p 42 - 44.
828.